# A2 - ProblemSet#2 Distributed:29January2010...

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Ch 24a Winter Term 2009 10 Introduction to Biophysical Chemistry Problem Set # 2 Distributed: 29 January 2010 Due: 8 February 2010, 1 p.m. 1. (25 points) (a) The π π * transition of the amino acid tryptophan in aqueous solution at pH 5 to 7 peaks at 220 nm with an extinction coefficient ε of 3.5 x 10 4 and a half width at half height of ~ 10 nm. Assume that the absorption band can be approximated by a Gaussian in frequency space and estimate the Einstein coefficient A for spontaneous fluorescence in sec 1 . (20 points) (b) Use the result above to calculate the intrinsic fluorescence lifetime of tryptophan, namely, the radiative lifetime τ R . If the quantum yield φ F for tryptophan in a protein is 0.3, what will be the corresponding fluorescence decay time τ F ? ( 5 points )

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a ) v = c / λ = 3 10 10 /(220 10 7 ) = 1.36 10 15 sec 1 to desicribe ε ( v ), one needs: v a = c / λ = 3 10 10 /(210 10 7 ) = 1.428 10 15 sec 1 v b = c / λ = 3 10 10 /(230 10 7 ) = 1.304 10 15 sec 1 Full width at half maximum for a gaussian function = 2 2ln2 σ = v a v b = 0.1243 10 15 σ = 5.266 10 13 ε ( v ) = 3.5 10 4 e ( v 1.36 10 15 ) 2 2 (5.266 10 13 ) 2 A = 8000 π v 3 Nc 2 log e ε ( v ) v band dv = 8000 π (1.36 10 15 ) 3 6 10 23 (3 10 10 ) 2 0.434 3.5 10 4 exp ( v 1.36 10 15 ) 2 2 (5.266 10 13 ) 2 v −∞ dv = 9.13 10 8 molecule/sec b ) τ R = 1 A = 1.09 10 9 sec τ F = 0.3 τ R = 3.28 10 10 sec 2. (10 points) For bacterial reaction centers, the quantum yield of fluorescence from the excited state of the special pair, a highly interacting pair of bacteriochlorophylls, is 10 4 . The intrinsic or natural radiative decay rate of the bacteriochlororphyll dimer is 10 8 sec 1 . Assuming that there are no non radiative processes other than electron transfer, what is the rate of transfer of an electron from the excited state of the bacteriochlorophyll dimer to the bacteriochlorophyll monomer before it is transferred to the bacteriopheophytin and subsequently to the primary quinone.
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